D&D 5E Point Buy vs Rolling for Stats

[Arial Black]

What are the odds of a 3 or 18 with 3d6?

OK, a bit of a tangent because I was trying to do math in my head last night. I know the odds of rolling a 3 or 18 on 3d6 is 1/216 because the odds of rolling any particular number is 1/6. Since we don't care about sequence these are independent events or 1/6 X 1/6 X 1/6 = 1/216.

Basic math, right? But what if I was curious about the extremes? Odds of a 3 or an 18? Once again, seems simple: (1/6 X 1/6 X 1/6) + (1/6 X 1/6 X 1/6) = 2/216 or 1/108.

So even in a village with 108 adults you're going to have 1 person that is at the normal maximum human potential for a particular stat and one at the absolute minimum.

But why stop there? There are 6 ability scores, so the odds of getting a 3 or 18 in one of those ability scores should be 6/108 or 1/18. Which means that in any random group of 18 people you will have (ignoring people that have multiple 18s or 3s) 1 person that as the min and max for every ability score.

What's wrong with my math? Or is rolling 3d6 for ability scores even more unrealistic than I thought?

You're doing it the wrong way round.

It's not that 'in every village of 216 people, 1 is the (joint) strongest man in the world'.

The correct interpretation is simply that in every {statistically average) village of 216 people then one of them will have 18 Str.

It is wrong to conclude that the starting maximum of 18 on 3d6 means that the 'highest stat in the world' is 18. The highest Str score in your world may be 24 for that 20th level barbarian, or 26 if he wants to read that book instead of eat it.

 

[Arial Black]

Are you honestly trying to use Xena as support for your "realism" argument?

Yes I am!

Because 'realism' is not the same as 'identical to real life'.

It just means 'realistic', as in 'things make sense and have logical consequences'.

And we are not using 'real life' as our goal for the amount of desired 'realism', we are using fantasy TV shows and films and books. Like Xena. Like Tolkien. Like Moorcock.

It is unrealistic (fatally for me) that every person in the group is as exactly capable as any other.

Also, character creation has a beginning (rolling? Concept?), and and end (the completed PC). The only 'balance' given by point-buy array comes somewhere during character creation (stats) but by the time the process is complete then it is no longer balanced (system mastery, SAD versus MAD, utility of different stats to different PCs, etc).

It seems an absurd bar that the point where balance has to be enforced must be part way through character creation!

 

[Caliban]

Yes I am!

And that is why I can't take you seriously.

Because 'realism' is not the same as 'identical to real life'.

It just means 'realistic', as in 'things make sense and have logical consequences'.

That is not what realistic means.

And we are not using 'real life' as our goal for the amount of desired 'realism', we are using fantasy TV shows and films and books. Like Xena. Like Tolkien. Like Moorcock.

You keep using "we" when you make your arguments. Please stop doing that - it makes an assumption that I find kind of offensive. I'm not part of this "we" who does things the way you do, and talking as if I am is manipulative.

It is unrealistic (fatally for me) that every person in the group is as exactly capable as any other.

That's your preference, and a reason why you shouldn't use point buy. (Except you've already admitted that you do... so it's not all that "fatal" for you.)

And even with point buy, not every person in the group is exactly as capable as any other. Characters within a group tend to focus on different things, and so are capable in different areas. The wizard isn't as capable as the fighter at melee combat or athletics (unless you are choosing to do something unusual - which is the strength of point buy. You can choose.)

Also, character creation has a beginning (rolling? Concept?), and and end (the completed PC). The only 'balance' given by point-buy array comes somewhere during character creation (stats) but by the time the process is complete then it is no longer balanced (system mastery, SAD versus MAD, utility of different stats to different PCs, etc).

It seems an absurd bar that the point where balance has to be enforced must be part way through character creation!

Well, that is a failure to understand on your part, not a failure of the method of character creation.

You keep talking as if your personal preferences are universal truths. They aren't.

 

[Oofta]

You're doing it the wrong way round.

It's not that 'in every village of 216 people, 1 is the (joint) strongest man in the world'.

The correct interpretation is simply that in every {statistically average) village of 216 people then one of them will have 18 Str.

It is wrong to conclude that the starting maximum of 18 on 3d6 means that the 'highest stat in the world' is 18. The highest Str score in your world may be 24 for that 20th level barbarian, or 26 if he wants to read that book instead of eat it.

I never said strongest man in the world. From the definition of what ability scores mean, an 18 is as high as a person can normally achieve and is something many people can achieve.

I don't think it's realistic that in every village of 100 people you have someone who is at both extremes, it certainly doesn't seem right that you only need 18 people to get the extremes of any given ability score and wanted someone to double check the math. That's all.

 

[Satyrn]

Actually, you might be surprised.
Which makes it ring truer to most D&D games than any other show out there, as most D&D settings take variants on historical real-world cultures from all sorts of eras - ancient Sumerians, classical Greeks, Romans, Vikings, Druidic-era Celts, Aztecs/Incans, right through middle-ages crusaders all the way up to early-Renaissance European - and put them all on the same world at the same time.

That describes Xena, though you left out Wuxia China and feudal Japan. It might be that those druidic Celts only appeared in Hercules, and I don't remember any Native Americans - oh, but there were modern Americans.

 

[Tony Vargas]

I never said strongest man in the world.

To tie for 'strongest man in the world,' even if human, he'd just have to have rolled an 18, and gained 4 levels so he could put his ASI into STR. Boom, one of the millions of strongest men in the world.

Assuming everyone's randomly rolled. Assuming everyone gets, at most, a closest-fit NPC block from the MM unless they're 'important' to the DM's campaign, not s'much.

All the rearranging of stats, choosing your race/background/class, etc. are not meant to represent that the PCs we play actually had control over those things.

Neither is assigning points to point buy /meant/ to represent the character controlling his stats.

It's just that those sufficiently demanding of the verisimilitude of the player making the same decisions on the same information as the imagined character, tend to see it that way, and it's thus 'unrealistic.' FWIW.

What they represent is that we, as players, could hypothetically scour the character sheets of the playable population of the world and choose what we want to play.

Sure, I suppose it could 'represent' that, though that's not really representing anything in the sense that modeling something can be realistic or unrealistic - there's nothing being modeled.

What constitutes 'playable' varies with method and instance. In any given instance of random-and-arrange, you're choosing from the small sub-set that have exactly the six numbers you rolled (a smaller meaningful sub-set if you rolled the same number two or more times). In each and every instance of array, from the similarly-sized sub-set that have exactly the array numbers (which at least are all different). In point-buy, in each instance, from the considerably larger sub-set that have any one of the various arrays that you can build using that method.

But, in all cases, those sub-sets are plausibly contained in the hypothetical population, given the range of stats (3-20) theoretically possible for PC races in 5e. How - and, more cogently, whether, since doing so would be prohibitive - that population's stats might be generated notwithstanding.

 

[Oofta]

To tie for 'strongest man in the world,' even if human, he'd just have to have rolled an 18, and gained 4 levels so he could put his ASI into STR.

Which is circular logic. That does not make it "realistic", it's just a conclusion drawn from the arbitrary 3d6 is how you get ability scores rule.

 

[Satyrn]

Ahhh! Xena: Warrior Princess! Hercules! Great shows! Typical D&D fodder!

Who were the 'player characters' here? Hercules, Iolus, Xena, Gabrielle, Joxer, a few others.

Would anyone like to try to convince me that Hercules and Xena were made to the same point-buy total as Joxer? Or even Gabrielle?

No, I wouldn't begin to try to convince you of that. But I will argue vehemently that Joxer was not a PC. He was the DM's comic relief NPC, created to give his little brother a way to join in without needing go pay attention to the story or any ongoing thing.

Autolycus and Salmoneus were played by the couple who were old friends of the group, but lived out of town and could only make to a session like twice a year.

 

[Tony Vargas]

Which is circular logic.

I still haven't denied that.

That does not make it "realistic", it's just a conclusion drawn from the arbitrary 3d6 is how you get ability scores rule.

It makes it un-realistic, doesn't it? Strongest-men-in-the-world aren't that common, right?

...so, yeah, it's really starting to look like the margin by which random (especially random-and-arrange) is 'more realistic' is actually pretty trivial.

 

[Oofta]

I still haven't denied that. It makes it un-realistic, doesn't it? Strongest-men-in-the-world aren't that common, right?

...so, yeah, it's really starting to look like the margin by which random (especially random-and-arrange) is 'more realistic' is actually pretty trivial.

Maybe it's because I write software, but the biggest issue with the "realism" argument is that we don't have any way of measuring what a realistic result would look like.

I have no clue how many people have an 18+ (or a 3) in any given ability score. I have a gut feeling that 1 in 216 vastly overstates the percentage. I've met people (family of a friend) that were severely mentally handicapped and would probably qualify for lowest possible intelligence a human can have. They are fortunately quite rare, much rarer than 1 in 216.

With no way to know what the target percentages should be, there is no way to model a method that would give you accurate results.